Influence of Evolutionary Allometry on Rates of Morphological Evolution and Disparity in strictly Subterranean Moles (Talpinae,Talpidae, Lipotyphla,Mammalia)

The adaptation to a particular function could directly influence the morphological evolution of an anatomical structure as well as its rates. The humeral morphology of moles (subfamily Talpinae) is highly modified in response to intense burrowing and fully fossorial lifestyle. However, little is known of the evolutionary pathways that marked its diversification in the two highly fossorial moles tribes Talpini and Scalopini. We used two-dimensional landmark-based geometric morphometrics and comparative methods to understand which factors influenced the rates and patterns of the morphological evolution of the humerus in 53 extant and extinct species of the Talpini (22 extant plus 12 extinct) and Scalopini (six extant plus 13 extinct) tribes, for a total of 623 humeri. We first built a synthetic phylogeny of extinct and extant taxa of the subfamily Talpinae based on all the available information from known phylogenies, molecular data, and age ranges of fossil records. We tested for evolutionary allometry by means of multivariate regression of shape on size variables. Evolutionary allometric trajectories exhibited convergence of humeral shape between the two tribes, even when controlling for phylogeny, though a significant differences in the evolutionary rates was found between the two tribes. Talpini, unlike Scalopini, seem to have reached a robust fossorial morphology early during their evolution, and their shape disparity did not change, if it did not decrease, through time. Furthermore, the basal Geotrypus spp. clearly set apart from the other highly fossorial moles, exhibiting a significant acceleration of evolutionary shifts toward higher degree of fossorial adaptation. Our observations support the hypothesis that the evolution of allometry may reflect a biological demand (in this case functional) that constrains the rates of evolution of anatomical structures.     

Divergence time estimation using fossils as terminal taxa and the origins of Lissamphibia

Were molecular data available for extinct taxa, questions regarding the origins of many groups could be settled in short order. As this is not the case, various strategies have been proposed to combine paleontological and neontological data sets. The use of fossil dates as node age calibrations for divergence time estimation from molecular phylogenies is commonplace. In addition, simulations suggest that the addition of morphological data from extinct taxa may improve phylogenetic estimation when combined with molecular data for extant species, and some studies have merged morphological and molecular data to estimate combined evidence phylogenies containing both extinct and extant taxa. However, few, if any, studies have attempted to estimate divergence times using phylogenies containing both fossil and living taxa sampled for both molecular and morphological data. Here, I infer both the phylogeny and the time of origin for Lissamphibia and a number of stem tetrapods using Bayesian methods based on a data set containing morphological data for extinct taxa, molecular data for extant taxa, and molecular and morphological data for a subset of extant taxa. The results suggest that Lissamphibia is monophyletic, nested within Lepospondyli, and originated in the late Carboniferous at the earliest. This research illustrates potential pitfalls for the use of fossils as post hoc age constraints on internal nodes and highlights the importance of explicit phylogenetic analysis of extinct taxa. These results suggest that the application of fossils as minima or maxima on molecular phylogenies should be supplemented or supplanted by combined evidence analyses whenever possible.     

Advances in the use of DNA barcodes to build a community phylogeny for tropical trees in a Puerto Rican forest dynamics plot

Background

Species number, functional traits, and phylogenetic history all contribute to characterizing the biological diversity in plant communities. The phylogenetic component of diversity has been particularly difficult to quantify in species-rich tropical tree assemblages. The compilation of previously published (and often incomplete) data on evolutionary relationships of species into a composite phylogeny of the taxa in a forest, through such programs as Phylomatic, has proven useful in building community phylogenies although often of limited resolution. Recently, DNA barcodes have been used to construct a robust community phylogeny for nearly 300 tree species in a forest dynamics plot in Panama using a supermatrix method. In that study sequence data from three barcode loci were used to generate a well-resolved species-level phylogeny.

Methodology/Principal Findings

Here we expand upon this earlier investigation and present results on the use of a phylogenetic constraint tree to generate a community phylogeny for a diverse, tropical forest dynamics plot in Puerto Rico. This enhanced method of phylogenetic reconstruction insures the congruence of the barcode phylogeny with broadly accepted hypotheses on the phylogeny of flowering plants (i.e., APG III) regardless of the number and taxonomic breadth of the taxa sampled. We also compare maximum parsimony versus maximum likelihood estimates of community phylogenetic relationships as well as evaluate the effectiveness of one- versus two- versus three-gene barcodes in resolving community evolutionary history.

Conclusions/Significance

As first demonstrated in the Panamanian forest dynamics plot, the results for the Puerto Rican plot illustrate that highly resolved phylogenies derived from DNA barcode sequence data combined with a constraint tree based on APG III are particularly useful in comparative analysis of phylogenetic diversity and will enhance research on the interface between community ecology and evolution.     

Molecular phylogenetics and biogeography of Lepus in Eastern Asia based on mitochondrial DNA sequences

In spite of several classification attempts among taxa of the genus Lepus, phylogenetic relationships still remain poorly understood. Here, we present molecular genetic evidence that may resolve some of the current incongruities in the phylogeny of the leporids. The complete mitochondrial cytb, 12S genes, and parts of ND4 and control region fragments were sequenced to examine phylogenetic relationships among Chinese hare taxa and other leporids throughout the World using maximum parsimony, maximum likelihood, and Bayesian phylogenetic reconstruction approaches. Using reconstructed phylogenies, we observed that the Chinese hare is not a single monophyletic group as originally thought. Instead, the data infers that the genus Lepus is monophyletic with three unique species groups: North American, Eurasian, and African. Ancestral area analysis indicated that ancestral Lepus arose in North America and then dispersed into Eurasia via the Bering Land Bridge eventually extending to Africa. Brooks Parsimony analysis showed that dispersal events followed by subsequent speciation have occurred in other geographic areas as well and resulted in the rapid radiation and speciation of Lepus. A Bayesian relaxed molecular clock approach based on the continuous autocorrelation of evolutionary rates along branches estimated the divergence time between the three major groups within Lepus. The genus appears to have arisen approximately 10.76 MYA (+/-0.86 MYA), with most speciation events occurring during the Pliocene epoch (5.65+/-1.15 MYA approximately 1.12 +/- 0.47 MYA).     

Big cat,small cat: reconstructing body size evolution in living and extinct Felidae

The evolution of body mass is a fundamental topic in evolutionary biology, because it is closely linked to manifold life history and ecological traits and is readily estimable for many extinct taxa. In this study, we examine patterns of body mass evolution in Felidae (Placentalia, Carnivora) to assess the effects of phylogeny, mode of evolution, and the relationship between body mass and prey choice in this charismatic mammalian clade. Our data set includes 39 extant and 26 extinct taxa, with published body mass data supplemented by estimates based on condylobasal length. These data were run through ‘SURFACE’ and ‘bayou’ to test for patterns of body mass evolution and convergence between taxa. Body masses of felids are significantly different among prey choice groupings (small, mixed and large). We find that body mass evolution in cats is strongly influenced by phylogeny, but different patterns emerged depending on inclusion of extinct taxa and assumptions about branch lengths. A single Ornstein–Uhlenbeck optimum best explains the distribution of body masses when first‐occurrence data were used for the fossil taxa. However, when mean occurrence dates or last known occurrence dates were used, two selective optima for felid body mass were recovered in most analyses: a small optimum around 5 kg and a large one around 100 kg. Across living and extinct cats, we infer repeated evolutionary convergences towards both of these optima, but, likely due to biased extinction of large taxa, our results shift to supporting a Brownian motion model when only extant taxa are included in analyses.     

PATTERNS IN PHYLOGENETIC TREE BALANCE WITH VARIABLE AND EVOLVING SPECIATION RATES

Aspects of phylogenetic tree shape, and in particular tree balance, provide clues to the workings of the macroevolutionary process. I use a simulation approach to explore patterns in tree balance for several models of the evolutionary process under which speciation rates vary through the history of diversifying clades. I demonstrate that when speciation rates depend on an evolving trait of individuals, and are therefore “heritable” along evolutionary lineages, the resulting phylogenies become imbalanced. However, imbalance also results from some (but not all) models of “nonheritable” speciation rate variation. The degree of imbalance increases with the magnitude of speciation rate variation, and then for gradual evolution (but not punctuated equilibria) reaches an asymptote short of the theoretical maximum. Very high levels of rate variation are required to produce imbalance matching that found in real data (estimated phylogenies from the systematic literature). I discuss implications of the simulation results for our understanding of macroevolution.     

Combined nuclear and mitochondrial DNA sequences resolve generic relationships within the Cracidae (Galliformes,Aves)

The Cracidae is one of the most endangered and distinctive bird families in the Neotropics, yet the higher relationships among taxa remain uncertain. The molecular phylogeny of its 11 genera was inferred using 10,678 analyzable sites (5,412 from seven different mitochondrial segments and 5,266 sites from four nuclear genes). We performed combinability tests to check conflicts in phylogenetic signals of separate genes and genomes. Phylogenetic analysis showed that the unrooted tree of ((curassows, horned guan) (guans, chachalacas)) was favored by most data partitions and that different data partitions provided support for different parts of the tree. In particular, the concatenated mitochondrial DNA (mtDNA) genes resolved shallower nodes, whereas the combined nuclear sequences resolved the basal connections among the major clades of curassows, horned guan, chachalacas, and guans. Therefore, we decided that for the Cracidae all data should be combined for phylogenetic analysis. Maximum parsimony (MP), maximum likelihood (ML), and Bayesian analyses of this large data set produced similar trees. The MP tree indicated that guans are the sister group to (horned guan, (curassows, chachalacas)), whereas the ML and Bayesian analysis recovered a tree where the horned guan is a sister clade to curassows, and these two clades had the chachalacas as a sister group. Parametric bootstrapping showed that alternative trees previously proposed for the cracid genera are significantly less likely than our estimate of their relationships. A likelihood ratio test of the hypothesis of a molecular clock for cracid mtDNA sequences using the optimal ML topology did not reject rate constancy of substitutions through time. We estimated cracids to have originated between 64 and 90 million years ago (MYA), with a mean estimate of 76 MYA. Diversification of the genera occurred approximately 41-3 MYA, corresponding with periods of global climate change and other Earth history events that likely promoted divergences of higher level taxa.     

Flies on thistles: support for synchronous speciation?

Synchronous speciation of hosts and herbivorous insects predicts a congruent topology of host and insect phylogenies and similar evolutionary ages of host and insect taxa. To test these predictions for the specialized herbivorous fly genus Urophora (Diptera: Tephritidae), we used three different approaches. (i) We generated a phylogenetic tree of 11 European Urophora species from allozyme data and constructed a phylogeny of their hosts from published sources. Superimposing the Urophora tree on the host-plant tree we found no evidence for general congruence. (ii) We correlated genetic distances (Nei distances) of the host plants vs. the genetic distances of associated Urophora species. Overall, the relationship was not positive. Nevertheless, for some pairs of Urophora species and host plants genetic distances were in the same order of magnitude. (iii) We collected allozyme data for pairs of thistle taxa and pairs of herbivores on thistles together with independent time estimates. With these data we calibrated a molecular clock. There was a non-linear relationship between phylogenetic age and genetic distance, rendering the dating of deep events in thistle–insect evolution difficult. Nevertheless the derived molecular clock showed that the split of insect taxa lagged behind the split of hosts.  © 2005 The Linnean Society of London, Biological Journal of the Linnean Society , 2005, 84 , 775–783.     

A mitogenomic timescale for birds detects variable phylogenetic rates of molecular evolution and refutes the standard molecular clock

Current understanding of the diversification of birds is hindered by their incomplete fossil record and uncertainty in phylogenetic relationships and phylogenetic rates of molecular evolution. Here we performed the first comprehensive analysis of mitogenomic data of 48 vertebrates, including 35 birds, to derive a Bayesian timescale for avian evolution and to estimate rates of DNA evolution. Our approach used multiple fossil time constraints scattered throughout the phylogenetic tree and accounts for uncertainties in time constraints, branch lengths, and heterogeneity of rates of DNA evolution. We estimated that the major vertebrate lineages originated in the Permian; the 95% credible intervals of our estimated ages of the origin of archosaurs (258 MYA), the amniote-amphibian split (356 MYA), and the archosaur-lizard divergence (278 MYA) bracket estimates from the fossil record. The origin of modern orders of birds was estimated to have occurred throughout the Cretaceous beginning about 139 MYA, arguing against a cataclysmic extinction of lineages at the Cretaceous/Tertiary boundary. We identified fossils that are useful as time constraints within vertebrates. Our timescale reveals that rates of molecular evolution vary across genes and among taxa through time, thereby refuting the widely used mitogenomic or cytochrome b molecular clock in birds. Moreover, the 5-Myr divergence time assumed between 2 genera of geese (Branta and Anser) to originally calibrate the standard mitochondrial clock rate of 0.01 substitutions per site per lineage per Myr (s/s/l/Myr) in birds was shown to be underestimated by about 9.5 Myr. Phylogenetic rates in birds vary between 0.0009 and 0.012 s/s/l/Myr, indicating that many phylogenetic splits among avian taxa also have been underestimated and need to be revised. We found no support for the hypothesis that the molecular clock in birds "ticks" according to a constant rate of substitution per unit of mass-specific metabolic energy rather than per unit of time, as recently suggested. Our analysis advances knowledge of rates of DNA evolution across birds and other vertebrates and will, therefore, aid comparative biology studies that seek to infer the origin and timing of major adaptive shifts in vertebrates.     

Step matrices and the interpretation of homoplasy

Assumptions about the costs of character change, coded in the form of a step matrix, determine most-parsimonious inferences of character evolution on phylogenies. We present a graphical approach to exploring the relationship between cost assumptions and evolutionary inferences from character data. The number of gains and losses of a binary trait on a phylogeny can be plotted over a range of cost assumptions, to reveal the inflection point at which there is a switch from more gains to more losses and the point at which all changes are inferred to be in one direction or the other. Phylogenetic structure in the data, the tree shape, and the relative frequency of states among the taxa influence the shape of such graphs and complicate the interpretation of possible permutation-based tests for directionality of change. The costs at which the most-parsimonious state of each internal node switches from one state to another can also be quantified by iterative ancestral-state reconstruction over a range of costs. This procedure helps identify the most robust inferences of change in each direction, which should be of use in designing comparative studies.     

Molecular phylogenies and divergence times of sea urchin species of Strongylocentrotidae,Echinoida

Sea urchins of the family Strongylocentrotidae have been important model systems in many fields of basic biology, yet knowledge of their evolutionary identities such as the phylogenetic relationships and divergence times remains limited. Here, I inferred molecular phylogenies of seven Strongylocentrotid species (Strongylocentrotus franciscanus, S. nudus, S. purpuratus, S. intermedius, S. droebachiensis, S. pallidus, and Hemicentrotus pulcherrimus) from the analyses of mitochondrial DNA sequences of 12SrDNA (349 nt), 12SrDNA-tRNA(gln) region (862 nt), and a combined sequence of cytochrome oxidase subunit I (COI, 1080 nt) and NADH dehydrogenase subunit I (NDI, 742 nt). The rate of sequence evolution and divergence times for each species were then estimated from the trees with reference to the time of separation between Strongylocentrotidae and Parechinidae, 35 to 50 MYA. The three trees agree well with each other, and the phylogeny is summarized by ((S. franciscanus, S. nudus), (H. pulcherrimus (S. purpuratus, S. intermedius (S. droebachiensis, S. pallidus)))). It is notable that the genus Strongylocentrotus consists of two distinct clades and that H. pulcherrimus branches off within Strongylocentrotus, implying assignment of a separate, monospecific genus to this species inappropriate. The rate of sequence evolution is calibrated to be 0.24%-0.34%/Myr in 12SrDNA, 0.25%-0.36%/Myr in 12SrDNA-tRNA(gln), and 0.65%-0.93%/Myr in COI-NDI combined sequences. S. purpuratus, in particular, shows the significantly higher rate of evolution in the 12SrDNA and 12SrDNA-tRNA(gln) regions compared to other species, suggesting careful use of its sequences in comparative studies. The two clades of Strongylocentrotidae seem to have split 13-19 MYA, and H. pulcherrimus branched off 7.2-14 MYA. In the former clade, S. franciscanus and S. nudus separated 5.7-8.1 MYA. In the latter clade, S. purpuratus, S. intermedius, and the clade of S. droebachiensis and S. pallidus diverged approximately 4.6-12 MYA, and the last two closest species separated 2.1-3.1 MYA.     

Mapping the Shapes of Phylogenetic Trees from Human and Zoonotic RNA Viruses

A phylogeny is a tree-based model of common ancestry that is an indispensable tool for studying biological variation. Phylogenies play a special role in the study of rapidly evolving populations such as viruses, where the proliferation of lineages is constantly being shaped by the mode of virus transmission, by adaptation to immune systems, and by patterns of human migration and contact. These processes may leave an imprint on the shapes of virus phylogenies that can be extracted for comparative study; however, tree shapes are intrinsically difficult to quantify. Here we present a comprehensive study of phylogenies reconstructed from 38 different RNA viruses from 12 taxonomic families that are associated with human pathologies. To accomplish this, we have developed a new procedure for studying phylogenetic tree shapes based on the ‘kernel trick’, a technique that maps complex objects into a statistically convenient space. We show that our kernel method outperforms nine different tree balance statistics at correctly classifying phylogenies that were simulated under different evolutionary scenarios. Using the kernel method, we observe patterns in the distribution of RNA virus phylogenies in this space that reflect modes of transmission and pathogenesis. For example, viruses that can establish persistent chronic infections (such as HIV and hepatitis C virus) form a distinct cluster. Although the visibly ‘star-like’ shape characteristic of trees from these viruses has been well-documented, we show that established methods for quantifying tree shape fail to distinguish these trees from those of other viruses. The kernel approach presented here potentially represents an important new tool for characterizing the evolution and epidemiology of RNA viruses.     

Phylogeny of Ptychopteroidea (Insecta: Diptera)

A phylogenetic tree is proposed for the superfamily Ptychopteroidea, reconstructed taking into account both extinct and extant taxa and based mainly on characters of wing venation.     

Discordant mtDNA and cpDNA phylogenies indicate geographic speciation and reticulation as driving factors for the diversification of the genus Picea

The phylogeny of the genus Picea was investigated by sequencing three loci from the paternally inherited chloroplast genome (trnK, rbcL and trnTLF) and the intron 2 of the maternally transmitted mitochondrial gene nad1 for 35 species. Significant topological differences were found between the trnK tree and the rbcL and trnTLF phylogenetic trees, and between cpDNA and mtDNA phylogenies. None of the phylogenies matched morphological classifications. The mtDNA phylogeny was geographically more structured than cpDNA phylogenies, reflecting the different inheritance of the two cytoplasmic genomes in the Pinaceae and their differential dispersion by seed only and seed and pollen, respectively. Most North American taxa formed a monophyletic group on the mtDNA tree, with topological patterns suggesting geographic speciation by range fragmentation or by dispersal and isolation. Similar patterns were also found among Asian taxa. Such a trend towards geographic speciation is anticipated in other Pinaceae genera with similar life history, autecology and reproductive system. Incongruences between organelle phylogenies suggested the occurrence of mtDNA capture by invading cpDNA. Incongruences between cpDNA partitions further suggested heterologous recombination presumably also linked to ancient reticulate evolution. Whilst cpDNA appears potentially valuable for molecular taxonomy and systematics purposes, these results emphasize the reduced value of cpDNA to infer vertical descent and the speciation history for plants with paternal transmission and high dispersal of their chloroplast genome.     

Morphological, palaeontological and molecular aspects of ichneumonoid phylogeny (Hymenoptera, Insecta)

Ichneumonoid phylogeny is revised on the basis of morphological, palaeontological and molecular evidence. The only previous formal cladistic study of the phylogeny of the families of the superfamily Ichneumonoidea made many assumptions about what families lower taxa belonged to and was based on a very limited set of characters, nearly all of which were uninformative at family level. We have subdivided both Ichneumonidae and Braconidae into major groups, investigated several new character systems, reinterpreted some characters, scored several character states for extinct taxa by examining impression fossils using environment chamber scanning electron microscopy, and included data for a significant new subfamily of Braconidae from Cretaceous amber of New Jersey. Sixteen different variants of the data set were each subjected to parsimony analysis without weighting and with successive approximations weighting employing both maximum and minimum values of both the retention and rescaled consistency indices. Each analysis resulted in one of seven different strict consensus trees. Consensus trees based on subsets of these trees, selected on the basis of the optimal character compatibility index (OCCI), resulted in an eighth distinct tree. All trees had the Braconidae monophyletic with the Trachypetinae as the basal clade, and also had a clade comprising various arrangements of Apozyginae, the Rhyssalinae group, Aphidiinae and 'other cyclostomes', but relationships among the remaining braconid groups varied between trees. Only one of the consensus trees had the Ichneumonidae (including Tanychorella ) monophyletic. The Eoichneumonidae + Tanychora are the sister group the Braconidae in two of the consensus trees. Paxylommatinae were basal in the clade comprising the Eoichneumonidae + Tanychora and the Braconidae. The preferred tree, based on the highest OCCI was used for interpreting character state transitions.     

ADAPTIVE RADIATION AND THE TOPOLOGY OF LARGE PHYLOGENIES

The idea that some organisms possess adaptive features that make them more likely to speciate and/or less likely to go extinct than closely related groups, suggests that large phylogenetic trees should be unbalanced (more species should occur in the group possessing the adaptive features than in the sister group lacking such features). Several methods have been used to document this type of adaptive radiation. One problem with these attempts is that evolutionary biologists may overlook balanced phylogenies while focusing on a few impressively unbalanced ones. To overcome this potential bias, we sampled published large phylogenies without regard to tree shape. These were used to test whether or not such trees are consistently unbalanced. We used recently developed null models to demonstrate that the shapes of large phylogenetic trees: 1) are similar among angiosperms, insects, and tetrapods; 2) differ from those expected due to random selection of a phylogeny from the pool of all trees of similar size; and 3) are significantly more unbalanced than expected if species diverge at random, therefore, conforming to one prediction of adaptive radiation. This represents an important first step in documenting whether adaptive radiation has been a general feature of evolution.     

Rooting molecular trees: problems and strategies

In constructing phylogenies from molecular data both the composition of the ingroup and the choice of outgroup can strongly affect the chances of obtaining the correct topology. This is because tree topology and uneven rates of molecular evolution affect the ability of tree-building algorithms to find the correct tree. Outgroups can be added in one of two ways, either to a single sister clade (preferably the closest) or through addition of single taxa from different clades. On theoretical and empirical grounds the former strategy is shown to be much more beneficial, both in terms of redressing balance and reducing stemminess. For parsimony to perform well some selection of sequence data, through omission or weighting, is also often necessary to reduce levels of homoplasy.     

Phylogenetic estimates of diversification rate are affected by molecular rate variation

Molecular phylogenies are increasingly being used to investigate the patterns and mechanisms of macroevolution. In particular, node heights in a phylogeny can be used to detect changes in rates of diversification over time. Such analyses rest on the assumption that node heights in a phylogeny represent the timing of diversification events, which in turn rests on the assumption that evolutionary time can be accurately predicted from DNA sequence divergence. But there are many influences on the rate of molecular evolution, which might also influence node heights in molecular phylogenies, and thus affect estimates of diversification rate. In particular, a growing number of studies have revealed an association between the net diversification rate estimated from phylogenies and the rate of molecular evolution. Such an association might, by influencing the relative position of node heights, systematically bias estimates of diversification time. We simulated the evolution of DNA sequences under several scenarios where rates of diversification and molecular evolution vary through time, including models where diversification and molecular evolutionary rates are linked. We show that commonly used methods, including metric‐based, likelihood and Bayesian approaches, can have a low power to identify changes in diversification rate when molecular substitution rates vary. Furthermore, the association between the rates of speciation and molecular evolution rate can cause the signature of a slowdown or speedup in speciation rates to be lost or misidentified. These results suggest that the multiple sources of variation in molecular evolutionary rates need to be considered when inferring macroevolutionary processes from phylogenies.     

Comparing tree shapes: beyond symmetry

This paper describes two types of problems related to tree shapes, as well as algorithms that can be used to solve these problems. The first problem is that of comparing the similarity of the unlabelled shapes instead of merely their degree of balance, in a manner analogous to that routinely used to compare topologies for labelled trees. There are possible practical applications for this comparison, such as determining, based on tree shape similarity alone, whether the taxa in two phylogenies are likely to have a correspondence (e.g. hosts and parasites with high specificity). It is shown that tree balance is insufficient for this task and that standard measures of topological difference (Robinson–Foulds distances, SPR distances or retention indices of the matrices representing the trees, MRPs) can be easily adapted to the problem. The second type of problem is to determine whether taxa of uncertain matching unique to two different phylogenies could correspond to each other (e.g. the same species in larvae and adults of metamorphic animals, fossils known from different body parts). This second problem can be solved by either relabelling taxa in such a way that the number of consensus nodes is maximized, or relabelling taxa in such a way that the sum of the number of steps in the MRP of each tree mapped onto the other is minimum.